qml.pulse.pwc

pwc(timespan)

Takes a time span and returns a callable for creating a function that is piece-wise constant in time. The returned function takes arguments (p, t), where p is an array that defines the bin values for the function.

Creates a callable for defining a ParametrizedHamiltonian.

Parameters

timespan (Union[float, tuple(float, float)]) – The time span defining the region where the function is non-zero. If an integer is provided, the time span is defined as (0, timespan).

Returns

a function that takes two arguments: an array of trainable parameters, and a float defining the time at which the function is evaluated.

Return type

callable

The convenience function pwc essentially implements

def pwc(timespan):
    def wrapped(p, t):
        return p[int(t/len(p))]
    return wrapped

This function can be used to create a parametrized coefficient function that is piece-wise constant within the interval t, and 0 outside it.

When creating the callable, only the time span is passed. The number of bins and values for the parameters are set when params is passed to the callable. Each bin value is set by an element of the params array. The variable t is used to select the value of the parameter array corresponding to the specified time, based on the assigned binning.

params = jnp.array([1, 2, 3, 4, 5])
time = jnp.linspace(0, 10, 1000)
timespan=(2, 7)
y = qml.pulse.pwc(timespan)(params, time)
plt.plot(time, y, label=f"params={params}, timespan={timespan}")
plt.legend()
plt.show()

Warning

The final time in the time span indicates the time at which the function output switches from params[-1] to 0. As such, the above function returns 5 for a time slightly smaller than the final time in timespan, but it returns 0 for the final time itself:

>>> qml.pulse.pwc(timespan)(params, 6.999999)
Array(5., dtype=float32)

>>> qml.pulse.pwc(timespan)(params, 7.)
Array(0., dtype=float32)

Example

>>> timespan = (2, 7)
>>> f1 = qml.pulse.pwc(timespan)
>>> H = f1 * qml.X(0)

The resulting function f1 has the call signature f1(params, t). If passed an array of parameters and a time, it will assign the array as the constants in the piece-wise function, and select the constant corresponding to the specified time, based on the time interval defined by timespan.

In the following example, passing an array to pwc((2, 7)) evenly distributes the array values in the interval t=2 to t=7. The time t is then used to select one of the array values based on this distribution.

>>> H(params=[[11, 12, 13, 14, 15]], t=2.3)
11.0 * X(0)

>>> H(params=[[11, 12, 13, 14, 15]], t=2.5) # different time, same bin, same result
11.0 * X(0)

>>> H(params=[[11, 12, 13, 14, 15]], t=3.1) # next bin
12.0 * X(0)

>>> H(params=[[11, 12, 13, 14, 15]], t=8) # outside the window returns 0
0.0 * X(0)

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